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## Homework Statement

Consider the truncated cone tank submerged in water: inside the truncated cone tank there is air. Evaluate the forces acting on the truncated cone tank.

## Homework Equations

## The Attempt at a Solution

The forces are the following

- Boyuant force : $$F_b= \rho_w g V_{tank}$$
- Weight $$P=m g $$
- Normal reaction $$N$$
**Pressure force**

I would have calculated it as follows.

$$F_p= F_{p \, on \, upper \, face}+F_{p \, on \, sides \, , y \, component}$$With ##F_{p \, on \, upper \, face}=\rho_W g (L-h) \pi R_2^2## and ##F_{p \, on \, sides \, , y \, component}= \int p(y) dS## (the last integral is for a force on a curved submerged surface so it is not very easy to calculate)

So what is the correct expression for the

**pressure force**on the tank?